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Attitude and Trajectory Estimation for Small Suborbital Payloads

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Attitude and Trajectory Estimation for Small Suborbital Payloads Attitude and Trajectory Estimation for Small Suborbital Payloads YUNXIA YUAN Doctoral Thesis Stockholm, Sweden 2017 TRITA-EE 2017:046 KTH School of Electrical Engineering ISSN 1653-5146 SE-100 44 Stockholm ISBN 978-91-7729-427-6 SWEDEN Akademisk avhandling som med tillstånd av Kungl Tekniska högskolan framlägges till offentlig granskning för avläggande av teknologie doktorsexamen i flyg- och rymdteknik 14:00 fredagen den 2 Juni 2017 i Q2, Osquldas väg 10, Stockholm. © Yunxia Yuan, June 2017 Tryck: Universitetsservice US AB iii Abstract Sounding rockets and small suborbital payloads provide a means for research in situ of the atmosphere and ionosphere. The trajectory and the attitude of the payload are critical for the evaluation of the scientific measurements and experiments. The trajectory refers the location of the measurement, while the attitude determines the orientation of the sensors. This thesis covers methods of trajectory and attitude reconstruction imple- mented in several experiments with small suborbital payloads carried out by the Department of Space and Plasma Physics in 2012–2016. The problem of trajectory reconstruction based on raw GPS data was studied for small suborbital payloads. It was formulated as a global least squares op- timization problem. The method was applied to flight data of two suborbital payloads of the RAIN REXUS experiment. Positions and velocities were ob- tained with high accuracy. Additionally, wind up rates were obtained, which match the measurements from onboard angular rate sensors. Based on the trajectory reconstruction technique, atmospheric densities, tem- peratures, and horizontal wind speeds below 80 km were obtained using rigid free falling spheres of the LEEWAVES experiment. An iterative method was applied using the relation between the retrieved accelerations and the veloc- ities and the densities. The dependence of the drag coefficient on the flow characteristics calls for the iterative approach. The uncertainties of the re- sults are lower at low altitudes. Comparison with independent data indicates that the results are reliable for densities below 70 km, temperatures below 50 km, and wind speeds below 45 km. Attitude reconstruction of suborbital payloads from yaw-pitch-roll Euler an- gles was studied, using measurements of magnetic fields and angular veloci- ties. The Euler angles were established by two methods: a global optimization method and an Unscented Kalman Filter (UKF) technique. The comparison of the results shows that the global optimization method provides a more accurate fit to the observations than the UKF. Improving the results of the falling sphere experiments requires understanding of the attitude motion of the sphere. An analytical consideration was devel- oped for a free falling and axisymmetric sphere under aerodynamic torques. Due to the displacement between the center of mass and the geometric cen- ter, the motion can generally be defined as a superposition of precession and nutation. These motion phenomena were modeled numerically and compared to flight data. iv Sammanfattning Sondraketer är en viktig teknik som används inom atmosfärs- och jonosfärs- forskningen. Nyttolastens bana och attityd är av vikt för experimenten och de vetenskapliga mätningarna, då banan beskriver var mätningarna togs vid en viss tidpunkt och attityden beskriver sensorns orientering. Denna avhandling omfattar metoder för rekonstruktion av nyttolasters banor och attityder i flera sondraketexperiment utförda av rymd- och plasmafysi- kavdelningen 2012–2016. Problemet med banrekonstruktion baserad på insamlade GPS-signaler har studerats för små friflygande sondraketnyttolaster. Det har formulerats som ett globalt minstakvadrat-optimeringsproblem. Metoden har applicerats på flygdata från två friflygande enheter i REXUS-experimentet RAIN. Positio- ner och hastigheter har erhållits med hög noggrannhet. Dessutom har en uppskattning gjorts på fasvridningen hos GPS-signalens bärvåg, som stäm- mer överens med vinkelhastighetsmätningar från en ombordsensor. Banrekonstruktionstekniken har använts för att bestämma atmosfärens tät- het, temperatur och vindhastighet från GPS data ombord på fallande sfärer inom LEEWAVES-experimentet. En iterativ metod har använts som grundar sig på relationen mellan tätheten och de rekonstruerade värdena på accelera- tion och hastighet. Det iterativa tillvägagångssättet är nödvändigt på grund av att luftmotståndet beror av flödesparametrarna på ett icke-linjärt sätt. Jämförelser med oberoende data indikerar att resultaten är pålitliga för at- mosfärstätheter under 70 km, temperaturer under 50 km och vindhastigheter under 45 km höjd. Attitydrekonstruktionen i form av gir-lutning-roll Eulervinklarna för en fri- flygande enhet har undersökts genom att använda mätningar av magnetfält och vinkelhastigheter. Två metoder användes för att rekonstruera Eulervink- larna: en global optimeringsmetod och unscented Kalmanfilterteknik (UKF). Jämförelsen av resultaten visar att den globala optimeringsmetoden ger en bättre överensstämmelse med observationerna än UKF. Förbättringar av resultaten från experimenten med fallande sfärer kräver för- ståelse av sfärens attitydrörelse. En analytisk modell har utvecklats för en fritt fallande och axisymmetrisk sfär under påverkan av aerodynamiska vridmo- ment. På grund av förskjutningen mellan masscentrum och det geometriska centrum kommer rörelsen generellt att vara en kombination av precession och nutation. Detta rörelsemönster har modellerats numeriskt och jämförts med flygdata. v Acknowledgements I would like to express my sincere and deep gratitude to my supervisor Dr. Nick- olay Ivchenko. Firstly, I thank him for giving me this opportunity to pursue a PhD under his supervision. During the period of study, Nickolay gave me enough freedom to conduct the research. He helped me plan my PhD study and research carefully, making it well-organised. He was always able to give detailed instructions whenever I came across difficulties, he supported me to learn more about what I was interested in and provided me with opportunities to improve myself in various ways, such as by taking part in practical projects, interesting courses, conferences and symposiums, learn how to express myself in writing and developing my com- puter and network skills. He is a very intelligent and knowledgeable scientist, whom I really admire. I am very grateful to my co-supervior Dr. Gunnar Tibert as well. He provided me with a great number of instructions in the beginning of my studies at KTH to help me conduct the PhD studies. His careful and meticulous research attitude influenced me largely. He kept his concern for my study and research, and spent much time to discuss my study and research. During the whole study period, he taught me much knowledge and many skills. Many thanks to my colleagues in the Department of Space and Plasma Physics, School of Electrical Engineering, KTH Royal Institute of Technology: Lars Bylan- der, Hanna Dahlgren, Gabriel Giono, Chunqing Huo, Tobias Kuremyr, Bin Li, Per- Arne Lindqvist, Göran Marklund, Georgi Olentsenko, Lorenz Roth, Nicola Manuel Schlatter, Peter Weijnitz. I thank them for their kind help and encouragement. Thanks to my fellows in Stockholm: Huina, Lin, Yan. I thank them for their warm help and company. My thanks also go to the Chinese Scholarship Council, which financially supported my PhD study. Last but not least, I really would like to express my deep appreciation to my par- ents. I thank them very much for their endless love and support, which has helped me to get through with these studies. Contents Contents vii Acronyms ix Paper list xi List of papers . xi Publications not included in this thesis . xi List of Figures xiii 1 Introduction 1 2 Sounding rocket and small satellite projects 3 2.1 RAIN . 3 2.2 MUSCAT . 5 2.3 SPIDER . 8 3 Principles of Global Navigation Satellite Systems 15 3.1 Signal . 15 3.2 Front end . 17 3.3 Software receiver operation . 17 3.4 Navigational solution . 19 4 Attitude kinematics and dynamics 21 4.1 Kinematics . 22 4.2 Attitude dynamics . 26 4.3 Euler’s equation . 28 5 State estimation 31 5.1 Least squares optimization . 31 5.2 Unscented transformation . 32 5.3 Unscented Kalman filter . 33 6 Results and conclusions 37 vii viii CONTENTS 6.1 Paper 1 . 37 6.2 Paper 2 . 38 6.3 Paper 3 . 39 6.4 Paper 4 . 39 Bibliography 41 Acronyms ADC Analog-to-Digital Converter BDU Boom Deployment Unit BPSK Binary Phase Shift Keying C/A code Coarse Acquisition code CU Common Unit DC Direct Current DCM Direction Cosine Matrix DLL Delay Lock Loop EMU Electric Measurement Unit EKF Expanded Kalman Filter ESA European Space Agency FFU Free Flight Units GPS Global Positioning System GNSS Global Navigation Satellite System IGS International GPS Service for Geodynamics KF Kalman Filter LEEWAVES Local Excitation and Effects of Waves on Atmospheric VErtical Structure LNA Low-Noise Amplifier MUSCAT MUltiple Spheres for Characterization of Atmospheric Temperatures P code Precision code ix x CONTENTS PCB Printed Circuit Board PGA Programmable Gain Amplifier PLL Phase Lock Loop QFN Quad Flat No-leads RAIN Rocket deployed Atmospheric probes conducting Independent measurements in Northern Sweden REXUS Rocket Experiments for University Students RMU Rocket Mounted Unit SPIDER Small Payloads for Investigation of Disturbances in Electrojet by Rockets TEM Transmission Electron Microscopy UHF Ultra High Frequency UKF Unscented Kalman Filter UT Unscented Transformation VCO Voltage Controlled Oscillator Paper list List of papers 1. Y. Yuan, E. Linden,
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